Question

Expand and state your answer as a polynomial in standard form. left bracket, 3, x, cubed, minus, y, cubed, right bracket, squared (3x 3 −y 3 ) 2

Answer 1

To expand the expression (3x^3 - y^3)^2, we need to multiply the expression by itself and then simplify to obtain 9x^6 - 6x^3y^3 + y^6.

Step-by-step explanation:

To expand the expression (3x^3 - y^3)^2, we need to multiply the expression by itself. Using the distributive property, we get (3x^3 - y^3)(3x^3 - y^3). We can then use the FOIL method to expand the expression.

F: Multiply the first terms, (3x^3)(3x^3) = 9x^6

O: Multiply the outer terms, (3x^3)(-y^3) = -3x^3y^3

I: Multiply the inner terms, (-y^3)(3x^3) = -3x^3y^3

L: Multiply the last terms, (-y^3)(-y^3) = y^6

Combining all the terms, we have 9x^6 - 3x^3y^3 - 3x^3y^3 + y^6. Simplifying, we get the final answer as 9x^6 - 6x^3y^3 + y^6.